I managed to solve the problem by deleting the following flash code from the file wp-admin\includes\media.php:
<?php if ( $flash ) : ?>
<script type="text/javascript">
<!--
jQuery(function($){
swfu = new SWFUpload({
upload_url : "<?php echo attribute_escape( $flash_action_url ); ?>",
flash_url : "<?php echo get_option('siteurl').'/wp-includes/js/swfupload/swfupload_f9.swf'; ?>",
file_post_name: "async-upload",
file_types: "<?php echo apply_filters('upload_file_glob', '*.*'); ?>",
post_params : {
"post_id" : "<?php echo $post_id; ?>",
"auth_cookie" : "<?php echo $_COOKIE[AUTH_COOKIE]; ?>",
"type" : "<?php echo $type; ?>",
"tab" : "<?php echo $tab; ?>",
"short" : "1"
},
file_size_limit : "<?php echo wp_max_upload_size(); ?>b",
swfupload_element_id : "flash-upload-ui", // id of the element displayed when swfupload is available
degraded_element_id : "html-upload-ui", // when swfupload is unavailable
file_dialog_start_handler : fileDialogStart,
file_queued_handler : fileQueued,
upload_start_handler : uploadStart,
upload_progress_handler : uploadProgress,
upload_error_handler : uploadError,
upload_success_handler : uploadSuccess,
upload_complete_handler : uploadComplete,
file_queue_error_handler : fileQueueError,
file_dialog_complete_handler : fileDialogComplete,
debug: false
});
$("#flash-browse-button").bind( "click", function(){swfu.selectFiles();});
});
//-->
</script>
<div id="flash-upload-ui">
<p><input id="flash-browse-button" type="button" value="<?php echo attribute_escape( __( 'Choose files to upload' ) ); ?>" class="button" /></p>
<p><?php _e('After a file has been uploaded, you can add titles and descriptions.'); ?></p>
</div>
<?php endif; // $flash ?>
I'm not sure if it's a good solution, but it seems to work after a few tests.